H_∞ output-feedback control of discrete-time systems with state-multiplicative noise

Linear discrete-time systems with stochastic uncertainties in their state-space model are considered. The problem of dynamic output-feedback control is solved via a new approach, for both the finite horizon and the stationary cases. In both cases, a cost function is defined which is the expected value of the standard H_∞ performance index with respect to the uncertain parameters. An example is given which demonstrates the applicability of the theory.